¶ … Value A."Suppose your bank account will be worth $15,000.00 in one year. The interest rate (discount rate) that the bank pays is 7%. What is the present value of your bank account today? What would the present value of the account be if the discount rate is only 4%?"

PV at 7%

=$15,000/1.07

=$14,018.69

With a discount rate of 7.00% of the bank account and a span of 1 year, the projected cash flows of my money are worth $0.07 today, and this is less than the initial $15,000.00. The resulting PV of the $15,000 is $14,018.69,

However, PV at 4%

=$15,000/1.04

=$14,423.08.

Interpretation

With a discount rate of 4.00% of my bank account with a span of 1 year, the projected cash flows are worth $0.08 today, which is less than the initial $15,000.00 money in the bank in one year. The resulting PV of the money in the bank in one year will be $14,423.08.

B. "Suppose you have two bank accounts, one called Account A and another Account B. Account A will be worth $6,500.00 in one year. Account B. will be worth $12,600.00 in two years. Both accounts earn 6% interest. What is the present value of each of these accounts?"

Answer

PV of Account A in one year

$6,500.00/1.06

= $6,132.08

PV of Account B. In 2 years

=$12,600/1.06 in the first year

=$11,886.79

In the second year:

=11886.79 / 1.06

=$11,213.96.

C. "Suppose you just inherited a gold mine. This gold mine is believed to have three years worth of gold deposit. Here is how much income this gold mine is projected to bring you each year for the next three years":

Year 1: $49,000,000

Year 2: $61,000,000

Year 3: $85,000,000

"Compute the present value of this stream of income at a discount rate of 7%. Remember, you are calculating the present value for a whole stream of income, i.e. The total value of receiving all three payments (how much you would pay right now to receive these three payments in the future). Your answer should be one number - the present value for this gold mine at a 7% discount rate but you have to show how you got to this number."

Answer

At 7% discount rate, the value of the gold mine is projected as follows:

=$49,000,000 / (1.07) + $61,000,000 / (1.07)2 + $85,000,000 / (1.07)3

= $45,794,392.52 + $53,279,762.42 + $69,385,319.54

=$168,459,474.48.

"Now compute the present value of the income stream from the gold mine at a discount rate of 5%, and at a discount rate of 3%. Compare the present values of the income stream under the three discount rates and write a short paragraph with conclusions from the computations."

Answer

PV of gold mine at 5%

=$49,000,000 / (1.05) + $61,000,000 / (1.05)2 + $85,000,000 / (1.05)3

=46,666,666.66 + 55,328,798.18 + 73,423,817.39

= $175,419,282.2

PV of gold mine at 3%

=$49,000,000 / (1.03) + $61,000,000 / (1.03)2 + $85,000,000 / (1.03)3

=47,572,815.53 + 57,498,350.46 + 77,787,041.05

=$182,858,207

Table 1 Comparison of the Present Value

First Year

Second Year

Third Year

Total

At 7%

$45,794,392.52

$53,279,762.42

$69,385,319.54

$168,459,474.48

At 5%

$46,666,666.66

$55,328,798.18

$73,423,817.39

$175,419,282.2

At 3%

47,572,815.53

57,498,350.46

77,787,041.05

$182,858,207

Comparison of the three discount rates reveals that the total PV of the gold mine at 3% within the three years is the highest with the total present value of $182,858,207. The total PV of 7% is the lowest that valued $168,459,474.48. However, at 5%, the PV is $175,419,282.2. Thus, the PV at the 3% is the best.

Part II

Based on the business plans of Interstate Travel Center, RJ Wagner & Associates Realty and Ice Dreams, the Interstate Travel Center carries the highest risks out of the three companies. The financial statements of the three companies are used to determine a company carrying highest risks out of the three companies. The paper uses the highest discount rate to evaluate which of the three project carrying highest level of risk. To determine which of the three companies carrying the highest risks, it is critical to calculate the net present value of the three companies using a discounted rate. Valuation using discounted rate is a financial strategy to determine the present value of a company using a future cash flow.

Interstate Travel Center

RJ Wagner & Associates Realty

Ice Dreams

Annual discount rate

10%

10%

10%

Initial Cost of Investment

$2,750,000

$60,000

$52,110

Return of First Year

$660,131

$32,750

$14,659

Return of Second Year

$709,578

$45,877

$28,595

Return of Third Year

$726,520

$75,277

$43,315

Cash Flow First Year

$489,669.00

34,747

$5,458

Cash Flow Second Year

$480,600.00

50,555

$20,681

Cash Flow Third Year

485816.00

83,401

$33,715

Net Present Value:

-$1,542,655.49

$76,029.62

-$4,725.83

PV of Expected Cash flows

$1,207,344.51

$136,029.62

$47,384.17

Interstate Travel Center

The Interstate Travel Center Net Present Value is -$1,542,655.49 and PV of Expected Cash flows of Interstate Travel Center are $1,207,344.51.

With a discount rate of 10.00% and a span of 3 years, your projected cash flows are worth $1,207,344.51 today, which is less than the initial $2,750,000.00 paid in order to begin. The resulting NPV of the above project is -$1,542,655.49, which means you will not receive the required return at the end of the project -- pursuing the above project may not be an optimal decision.

RJ Wagner & Associates Realty

Using the ratio analysis to compare the three companies, the Interstate Travel Center net profit margin remain the same year after year. In the first...

Moreover, the company returns on equity declines yearly. The ROE was 527% in the first year and decline stiffly to 85.01% in the second years. In the third year, the company ROE declined to 46.54%.
Similarly, the net profit margin of RJ Wagner & Associates Realty also decline from 24.19% in the first year, however, decline to 16.38% in the third year. Return on equity also decline from 55.04% in the first year to 41.67% in the third.

Contrarily, the net profit margin of Ice Dream increases yearly from 28.07% in the first year to 41.47% in the third year. Moreover, the return on equity increases from 0.0% in the first year to 71.53% in the third year.

The paper focuses on the Apple Inc. To answer the future price of Apple in next one year. Apple Inc. specializes in designing, manufacturing and marketing of portable computing products and personal computing products, which include iPhone, iPad, and desktop computers such as iMac, Mac Mini, Mac Pro and other software product such as OS X operating system and iOS.

Based on the company financial data, the paper addresses the following questions:

1."What do you think would the futures price of 100 shares of your reference company to be delivered to you in one year be right now?."

Answer

The present price of one share of Apple Inc. As of 13 June 2013 is $434.77, and 100 shares of $434.77 is $43,477.00.

To determine the price of Apple Inc. In next one year, it is critical to evaluate the historical prices of Apple Inc. shares in the last 10 years. Based on the historical prices of the company, the company price will increase in the next one year because Apple has demonstrated yearly increase in the share prices in the last 10 years. Although, the company recorded a slight decline in the share price between 2008 and 2009, and the major factor leading to the decline was due to a global financial crisis that occurred during the period, however, the future price of the 100 share prices of Apple Inc. will be $65,900

Apple Inc. 10-Year Historical Prices ($)

Year

Share Price

1

June 2013

2

June 2012

3

June 2011

4

June 2010

5

June 2009

6

June 2008

7

June 2007

8

June 2006

59.85

9

June 2005

39.89

10

June 2004

27.79

Source: Yahoo Finance 2013

Source: Yahoo Finance 2013

Based on the historical price of the Apple Inc., the share price of Apple in next one year will be much higher and the price will be $659.00. Moreover, the stock is less risky and it has been relative stable over the last 10-year. Overview of the company profitability ratios reveals that the company ROE (return on equity) provides a stable increase in the last 5 years. In 2008, the ROE was 27.19%, and the ROE increased to 33.34% in 2013. Similarly, return on asset (ROA) also provides a significant increase in the last 5 years.( BPlan, 2012).

The alternative investment is Treasury Notes, however, the rate my bank is giving me on saving account is 0.01%. However, if I am able to a get greater return on other investment, I will be unwilling to pay for future equity.

Apple Inc. Profitability Ratio

TTM

2012-09

2011-09

2010-09

2009-09

2008-09

2007-09

2006-09

2005-09

2004-09

2003-09

Tax Rate %

25.61

25.16

24.22

24.42

31.75

29.89

30.19

29.42

26.45

27.94

26.09

Net Margin %

23.46

26.67

23.95

21.48

19.19

14.88

14.56

10.30

9.58

3.33

1.11

Asset Turnover (Average)

0.98

1.07

1.13

1.06

0.99

1.00

1.13

1.34

1.42

1.11

0.95

Return on Assets %

22.95

28.54

27.07

22.84

18.92

14.89

16.43

13.83

13.62

3.71

1.05

Financial Leverage (Average)

1.44

1.49

1.52

1.57

1.50

1.88

1.74

1.72

1.55

1.59

1.61

Return on Equity %

33.34

42.84

41.67

35.28

31.27

27.19

28.52

22.80

21.29

5.94

1.66

Return on Invested Capital %

33.34

42.84

41.67

35.28

31.27

27.19

28.52

22.80

21.29

5.94

1.55

Interest Coverage

Conclusion

The paper demonstrates the application of present value in the determining the viability of a project. The first part of the paper compares the PV of different projects and based on the PV of the projects, the paper has been able to determine the project's viability. Moreover, the paper evaluates the PV of gold mine and based of the findings of the PV, it is revealed that the PV of 3% is the best. The part two of the project compares the viability of three companies and based on the results of the valuations, it is revealed that Interstate Travel Center carries the highest risks of returns for investors.